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Scalar Curvatures of Invariant Almost Hermitian Structures on Flag Manifolds with Two and Three Isotropy Summands

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Abstract

In this paper, we study invariant almost Hermitian geometry on generalized flag manifolds which the isotropy representation decompose into two or three irreducible components. We will provide a classification of such flag manifolds admitting Kähler like scalar curvature metric, that is, almost Hermitian structures (g, J) satisfying \(s=2s_C\) where s is Riemannian scalar curvature and \(s_C\) is the Chern scalar curvature.

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Acknowledgements

We would like to thank Leonardo Cavenaghi and Eder Correa for useful discussions. LG is partially supported by FAPESP Grants 2018/13481-0, 2021/04003-0, 2021/04065-6.

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Authors and Affiliations

  1. Departamento de Matemática, Imecc - Unicamp, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz, Campinas, SP, 13083-859, Brazil

    Lino Grama

  2. UEMS - Universidade Estadual de Mato Grosso do Sul - MS, Cidade UniversitÁria de Dourados, Rodovia Itahum, Km 12 s/n - Jardim Aeroporto, Dourados, MS, Brazil

    Ailton R. Oliveira

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  1. Lino Grama
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Correspondence to Lino Grama.

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Grama, L., Oliveira, A.R. Scalar Curvatures of Invariant Almost Hermitian Structures on Flag Manifolds with Two and Three Isotropy Summands. J Geom Anal 33, 311 (2023). https://doi.org/10.1007/s12220-023-01377-9

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